Relation Between Power and Resistance: Definition, Diagram, Sample Questions

Ans. The resistance is inversely proportional to the current, which is directly proportional to the voltage. This indicates that when the voltage is increased, the current increases, whereas as the resistance is increased, the current decreases.

Ans. Because the circuit's resistance has doubled, the current has been cut in half. This signifies that the battery's power output is half of what it was previously. However, the power is now split between two lights.

Ans. We must slow down our car some distance before the speed breakers if we are travelling at high speeds; else, our vehicle will jump with a lot of jerk. So, the maximum current flowing through the circuit (road) is represented by our high-speed vehicle, and the speed breaker represents the resistance that prevents accidents or short circuits in our homes.

Ans. We discovered six applications of Ohm's law in our daily lives.

• Electric Heaters
• Electric Kettles and Irons
• Design of Electric Devices
• Fuse Design
• Mobile or Laptop Charger
• Domestic Fans

Ans. We know the voltage and current for the hot headlamp, so we can use P = IV to calculate the power. We know the voltage and resistance for the cold headlight, thus we can calculate the power using P = V 2/R.

We get the current and voltage numbers for the hot headlamp by plugging in the known values.

P = IV = (2.50 A)(12.0 V) = 30.0 W.

Because the cold resistance was 0.350 Ω , the power it uses when it initially turns on is

P = V² / R = (12.0 V)² / 0.350 Ω = 411 W

Heated headlight dissipates 30 W, which is average. When it's cold, though, the 411 W is noticeably higher. As the bulb's temperature rises and its resistance rises, the initial power quickly drops.

Ans. We know the voltage and current for the hot bike headlight, so we can use P = IV to calculate the power. We know the voltage and resistance for the cold bike headlight, thus we can calculate the power using P = V²/R.

We get the current and voltage numbers for the hot bike headlight by plugging in the known values.

P = IV = (5.0 A)(24.0 V) = 120.0 W.

Because the cold resistance was 0.350 Ω , the power it uses when it initially turns on is

P = V² / R = (24.0 V) 2 / 0.350 Ω = 1645 W

The heated headlight dissipates 120 W, which is average. When it's cold, though, the 1645 W is noticeably higher. As the bulb's temperature rises and its resistance rises, the initial power quickly drops.

Ans. So, here we have given formula

Power = Work / time

In Case 1:

Work in form of energy is 30 J and Time is 2 hrs then

P = W/T = 30/2 = 15 W

In Case 2:

Work in form of energy is also 30 J but time is 3 hrs then

P = W/T = 30/2 = 10 W

We can see that individual A has more capability than person B. As a result, power A is bigger than power B.

Ans. a. Outlets are wired in parallel so that the appliances on a circuit are independent of one another. Turning the coffee maker off will not result in the toaster turning off (assuming both were on at the same time). Each appliance will also get the same regulated voltage, which simplifies the design of electrical devices. The downside to this scheme is that the parallel currents can add up to dangerously high levels. A circuit breaker in series before the parallel branches can prevent overload by automatically opening the circuit.

b. A 15 A circuit operating at 120 V consumes 1,800 W of total power.

P = VI = (120 V), (15 A) = 1,800 W

Total power in a parallel circuit is the sum of the power consumed on the individual branches.

coffee maker + microwave oven = 850 W + 1200 W = 2050 W

microwave oven + toaster = 1200 W + 900 W = 2100 W

toaster + coffee maker = 900 W + 850 W = 1750 W

On this circuit, only the coffee maker and toaster can be operated simultaneously. All other combinations will trigger the circuit breaker to open.

Ans. To find the power of the bulb:

• Electric Power: The rate at which electrical energy is dissipated into other forms of energy is called electrical power i.e.,

\(P = \frac{W}{t} = VI = {I^2}R = \frac{{{V^2}}}{R}\)

Where V = Potential difference, R = Resistance and I = current.

Given: Potential difference (V) = 220 V, power of the bulb (P) = 100 W and actual voltage (V') = 110 V

• The resistance of the bulb can be calculated as,

​\(\Rightarrow R=\frac{V^2}{P}=\frac{(220)^2}{100}=484 \,\Omega\)

• The power consumed by the bulb.

\(\Rightarrow P=\frac{V^2}{R}=\frac{(110)^2}{484}=25 \,W\)

Ans. Resistance of electric heater can be calculated as follows:

• Heating effect of electric current: When a current is flowing in a circuit having resistance there is a heat dissipation due to the resistance. This is called the heating effect of electric current.
• The heat dissipated is given by:

Heat (H) = I² R t

Where I = the current flowing in the circuit, R = the resistance of the circuit, and t = the time taken

Given that: current (I) = 2 A

Resistance = R

Heat dissipated = work done by the heater (H) = 200 J

Time (t) = 2 sec

Heat (H) = I² R t = 2² × R × 2 = 200 J

8 R = 200

Resistance of the heater (R) = 200/8 = 25 Ω

Ans. The electric charge can be calculated in the following way:

• Electric charge: It is an intrinsic property of the elementary particles of matter which gives rise to electric force between various objects.

It is a scalar quantity.

• SI unit of electric charge is coulomb (C).
• The total charge on the conductor is given by q = It, when current flows through the conductor for some time.

Where I = current and t = time

CALCULATION:

Given - I = 5 A and t = 2 min = 120 s

• The total charge on the conductor is given by q = It

⇒ Q = It

⇒ Q = 5 × 120 = 600 C

Ans. Resistivity of material depends on:

• The unit for resistivity is the ohm-meter (Ω-m).
• The resistivity of a material depends on its nature and the temperature of the conductor.
• The resistivity of a material doesn't depend on its shape and size (length and area).
• Materials that conduct electrical current easily are called conductors and have a low resistivity.
• Materials that do not conduct electricity easily are called insulators and these materials have a high resistivity.
• Resistivity is inversely proportional to the number of free electrons per unit volume of the conductor and to the average relaxation time of the free electrons in the conductor.

• Resistance: The property of any conductor that opposes the flow of electric current through it and depends on the shape and size of the materials, temperature, and nature of the materials is called resistance.
  • It is denoted by R and the SI unit is the ohm (Ω).

The resistance is given by:

R = ρL/A

where ρ is resistivity, L is the length and A is the area of the cross-section.

EXPLANATION:

From the above discussion, we can say that

1. The resistivity doesn't depend on the dimensions (length, diameter, and area) of the conductor.
2. The resistivity depends on the material of the conductor. So option 4 is correct.
3. The resistivity depends on the temperature of the conductor. But the effect of temperature is negligible.
4. The resistivity does not depend on the density of the conductor.